Generalized p,q-Gamma-type operators

Abstract

<jats:p>In the present paper, the generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:mfenced></mml:math>-gamma-type operators based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:mfenced></mml:math>-calculus are introduced. The moments and central moments are obtained, and some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi mathvariant="script">K</mml:mi></mml:math>-functional. Also, the rate of convergence, weighted approximation, and pointwise estimates of these operators are studied. Finally, a Voronovskaja-type theorem is presented.</jats:p>

Approximation Properties of a New Type of Gamma Operator Defined with the Help of k -Gamma Function

“…Then, in the literature, some researchers introduced the generalizations of Gamma and beta functions and also the extensions of Gamma-type operators and their extensions [5][6][7][8][9][10][11][12][13][14]. One of the studies of this topic was by Daz and Pariguan [15]; they introduced and researched k-Gamma function when they were assessing Feynman integrals.…”

Approximation Properties of New Modified Gamma Operators

“…In [11], Zhou et al extended the works of Cheng et al in [10] and constructed ðp, qÞ-Gamma-Stancu operators. There are many papers about the research and application of other Gamma-type operators, and we mention some of them [12][13][14][15][16][17].…”